Right, being poly (or poly-friendly) doesn't mean you have to be perfect. Everyone has their peculiar needs and limitations. I don't think you should just have to choke your worries down, they're not just your problem, you're in a relationship. I would keep a close eye on this partner's budding relationship with this competitive friend and put the brakes on it fast if it is beginning to overwhelm you.
Love means never having to say, "Put down that meat cleaver!"